# Definition > Let $C$ be a smooth curve parameterized by $\vec{r}(t)$ from $\vec{r}(a)=A$ to $\vec{r}(b)=B$ given a continuous vector field $\vec{F}=\nabla f$ > $\int_C\vec{F}\cdot d\vec{r}=f(B)-f(A)$ If a continuous vector field $\vec{F}$ can be written as the gradient of a potential function $f$, the integral along a smooth curve $C$ is given by the difference of the values of the potential function evaluated at the beginning and end points of the integral - Extension of the [[Fundamental Theorem of Calculus]] to [[Line Integrals|line integrals]]